Question

5x² + 6x + 1 = 0
master product: 5
answer attempt 1 out of 2
⊕ additional solution ⊖ no solution
x =

Explanation:

Step1: Factor the quadratic equation

We have the quadratic equation \(5x^2 + 6x + 1 = 0\). We need to find two numbers that multiply to \(5\times1 = 5\) and add up to \(6\). The numbers are \(5\) and \(1\). So we can rewrite the middle term:
\(5x^2 + 5x + x + 1 = 0\)

Step2: Group and factor

Group the first two terms and the last two terms:
\((5x^2 + 5x) + (x + 1) = 0\)
Factor out the common factors from each group:
\(5x(x + 1) + 1(x + 1) = 0\)
Now, factor out \((x + 1)\):
\((5x + 1)(x + 1) = 0\)

Step3: Solve for \(x\)

Set each factor equal to zero:

• \(5x + 1 = 0\) gives \(5x = -1\), so \(x = -\frac{1}{5}\)
• \(x + 1 = 0\) gives \(x = -1\)

Answer:

\(x = -1\) or \(x = -\frac{1}{5}\)